# MLIR

Multi-Level IR Compiler Framework

# 'affine' Dialect

This dialect provides a powerful abstraction for affine operations and analyses.

## Polyhedral Structures ¶

MLIR uses techniques from polyhedral compilation to make dependence analysis and loop transformations efficient and reliable. This section introduces some of the core concepts that are used throughout the document.

### Dimensions and Symbols ¶

Dimensions and symbols are the two kinds of identifiers that can appear in the polyhedral structures, and are always of index type. Dimensions are declared in parentheses and symbols are declared in square brackets.

Examples:

// A 2d to 3d affine mapping.
// d0/d1 are dimensions, s0 is a symbol
#affine_map2to3 = affine_map<(d0, d1)[s0] -> (d0, d1 + s0, d1 - s0)>


Dimensional identifiers correspond to the dimensions of the underlying structure being represented (a map, set, or more concretely a loop nest or a tensor); for example, a three-dimensional loop nest has three dimensional identifiers. Symbol identifiers represent an unknown quantity that can be treated as constant for a region of interest.

Dimensions and symbols are bound to SSA values by various operations in MLIR and use the same parenthesized vs square bracket list to distinguish the two.

Syntax:

// Uses of SSA values that are passed to dimensional identifiers.
dim-use-list ::= ( ssa-use-list? )

// Uses of SSA values that are used to bind symbols.
symbol-use-list ::= [ ssa-use-list? ]

// Most things that bind SSA values bind dimensions and symbols.
dim-and-symbol-use-list ::= dim-use-list symbol-use-list?


SSA values bound to dimensions and symbols must always have ‘index’ type.

Example:

#affine_map2to3 = affine_map<(d0, d1)[s0] -> (d0, d1 + s0, d1 - s0)>
// Binds %N to the s0 symbol in affine_map2to3.
%x = memref.alloc()[%N] : memref<40x50xf32, #affine_map2to3>


### Restrictions on Dimensions and Symbols ¶

The affine dialect imposes certain restrictions on dimension and symbolic identifiers to enable powerful analysis and transformation. An SSA value’s use can be bound to a symbolic identifier if that SSA value is either 1. a region argument for an op with trait AffineScope (eg. FuncOp), 2. a value defined at the top level of an AffineScope op (i.e., immediately enclosed by the latter), 3. a value that dominates the AffineScope op enclosing the value’s use, 4. the result of a constant operation, 5. the result of an affine.apply operation that recursively takes as arguments any valid symbolic identifiers, or 6. the result of a dim operation on either a memref that is an argument to a AffineScope op or a memref where the corresponding dimension is either static or a dynamic one in turn bound to a valid symbol. Note: if the use of an SSA value is not contained in any op with the AffineScope trait, only the rules 4-6 can be applied.

Note that as a result of rule (3) above, symbol validity is sensitive to the location of the SSA use. Dimensions may be bound not only to anything that a symbol is bound to, but also to induction variables of enclosing affine.for and affine.parallel operations, and the result of an affine.apply operation (which recursively may use other dimensions and symbols).

### Affine Expressions ¶

Syntax:

affine-expr ::= ( affine-expr )
| affine-expr + affine-expr
| affine-expr - affine-expr
| -? integer-literal * affine-expr
| affine-expr ceildiv integer-literal
| affine-expr floordiv integer-literal
| affine-expr mod integer-literal
| -affine-expr
| bare-id
| -? integer-literal

multi-dim-affine-expr ::= ( )
| ( affine-expr (, affine-expr)* )


ceildiv is the ceiling function which maps the result of the division of its first argument by its second argument to the smallest integer greater than or equal to that result. floordiv is a function which maps the result of the division of its first argument by its second argument to the largest integer less than or equal to that result. mod is the modulo operation: since its second argument is always positive, its results are always positive in our usage. The integer-literal operand for ceildiv, floordiv, and mod is always expected to be positive. bare-id is an identifier which must have type index. The precedence of operations in an affine expression are ordered from highest to lowest in the order: (1) parenthesization, (2) negation, (3) modulo, multiplication, floordiv, and ceildiv, and (4) addition and subtraction. All of these operators associate from left to right.

A multidimensional affine expression is a comma separated list of one-dimensional affine expressions, with the entire list enclosed in parentheses.

Context: An affine function, informally, is a linear function plus a constant. More formally, a function f defined on a vector $\vec{v} \in \mathbb{Z}^n$ is a multidimensional affine function of $\vec{v}$ if $f(\vec{v})$ can be expressed in the form $M \vec{v} + \vec{c}$ where $M$ is a constant matrix from $\mathbb{Z}^{m \times n}$ and $\vec{c}$ is a constant vector from $\mathbb{Z}$. $m$ is the dimensionality of such an affine function. MLIR further extends the definition of an affine function to allow ‘floordiv’, ‘ceildiv’, and ‘mod’ with respect to positive integer constants. Such extensions to affine functions have often been referred to as quasi-affine functions by the polyhedral compiler community. MLIR uses the term ‘affine map’ to refer to these multidimensional quasi-affine functions. As examples, $(i+j+1, j)$, $(i \mod 2, j+i)$, $(j, i/4, i \mod 4)$, $(2i+1, j)$ are two-dimensional affine functions of $(i, j)$, but $(i \cdot j, i^2)$, $(i \mod j, i/j)$ are not affine functions of $(i, j)$.

### Affine Maps ¶

Syntax:

affine-map-inline
::= dim-and-symbol-id-lists -> multi-dim-affine-expr


The identifiers in the dimensions and symbols lists must be unique. These are the only identifiers that may appear in ‘multi-dim-affine-expr’. Affine maps with one or more symbols in its specification are known as “symbolic affine maps”, and those with no symbols as “non-symbolic affine maps”.

Context: Affine maps are mathematical functions that transform a list of dimension indices and symbols into a list of results, with affine expressions combining the indices and symbols. Affine maps distinguish between indices and symbols because indices are inputs to the affine map when the map is called (through an operation such as affine.apply), whereas symbols are bound when the map is established (e.g. when a memref is formed, establishing a memory layout map).

Affine maps are used for various core structures in MLIR. The restrictions we impose on their form allows powerful analysis and transformation, while keeping the representation closed with respect to several operations of interest.

#### Named affine mappings ¶

Syntax:

affine-map-id ::= # suffix-id

// Definitions of affine maps are at the top of the file.
affine-map-def    ::= affine-map-id = affine-map-inline

// Uses of affine maps may use the inline form or the named form.
affine-map ::= affine-map-id | affine-map-inline


Affine mappings may be defined inline at the point of use, or may be hoisted to the top of the file and given a name with an affine map definition, and used by name.

Examples:

// Affine map out-of-line definition and usage example.
#affine_map42 = affine_map<(d0, d1)[s0] -> (d0, d0 + d1 + s0 floordiv 2)>

// Use an affine mapping definition in an alloc operation, binding the
// SSA value %N to the symbol s0.
%a = memref.alloc()[%N] : memref<4x4xf32, #affine_map42>

// Same thing with an inline affine mapping definition.
%b = memref.alloc()[%N] : memref<4x4xf32, affine_map<(d0, d1)[s0] -> (d0, d0 + d1 + s0 floordiv 2)>>


### Semi-affine maps ¶

Semi-affine maps are extensions of affine maps to allow multiplication, floordiv, ceildiv, and mod with respect to symbolic identifiers. Semi-affine maps are thus a strict superset of affine maps.

Syntax of semi-affine expressions:

semi-affine-expr ::= ( semi-affine-expr )
| semi-affine-expr + semi-affine-expr
| semi-affine-expr - semi-affine-expr
| symbol-or-const * semi-affine-expr
| semi-affine-expr ceildiv symbol-or-const
| semi-affine-expr floordiv symbol-or-const
| semi-affine-expr mod symbol-or-const
| bare-id
| -? integer-literal

symbol-or-const ::= -? integer-literal | symbol-id

multi-dim-semi-affine-expr ::= ( semi-affine-expr (, semi-affine-expr)* )


The precedence and associativity of operations in the syntax above is the same as that for affine expressions.

Syntax of semi-affine maps:

semi-affine-map-inline
::= dim-and-symbol-id-lists -> multi-dim-semi-affine-expr


Semi-affine maps may be defined inline at the point of use, or may be hoisted to the top of the file and given a name with a semi-affine map definition, and used by name.

semi-affine-map-id ::= # suffix-id

// Definitions of semi-affine maps are at the top of file.
semi-affine-map-def ::= semi-affine-map-id = semi-affine-map-inline

// Uses of semi-affine maps may use the inline form or the named form.
semi-affine-map ::= semi-affine-map-id | semi-affine-map-inline


### Integer Sets ¶

An integer set is a conjunction of affine constraints on a list of identifiers. The identifiers associated with the integer set are separated out into two classes: the set’s dimension identifiers, and the set’s symbolic identifiers. The set is viewed as being parametric on its symbolic identifiers. In the syntax, the list of set’s dimension identifiers are enclosed in parentheses while its symbols are enclosed in square brackets.

Syntax of affine constraints:

affine-constraint ::= affine-expr >= affine-expr
| affine-expr <= affine-expr
| affine-expr == affine-expr
affine-constraint-conjunction ::= affine-constraint (, affine-constraint)*


Integer sets may be defined inline at the point of use, or may be hoisted to the top of the file and given a name with an integer set definition, and used by name.

integer-set-id ::= # suffix-id

integer-set-inline
::= dim-and-symbol-id-lists : '(' affine-constraint-conjunction? ')'

// Declarations of integer sets are at the top of the file.
integer-set-decl ::= integer-set-id = integer-set-inline

// Uses of integer sets may use the inline form or the named form.
integer-set ::= integer-set-id | integer-set-inline


The dimensionality of an integer set is the number of identifiers appearing in dimension list of the set. The affine-constraint non-terminals appearing in the syntax above are only allowed to contain identifiers from dims and symbols. A set with no constraints is a set that is unbounded along all of the set’s dimensions.

Example:

// A example two-dimensional integer set with two symbols.
#set42 = affine_set<(d0, d1)[s0, s1]
: (d0 >= 0, -d0 + s0 - 1 >= 0, d1 >= 0, -d1 + s1 - 1 >= 0)>

// Inside a Region
affine.if #set42(%i, %j)[%M, %N] {
...
}


d0 and d1 correspond to dimensional identifiers of the set, while s0 and s1 are symbol identifiers.

## Operations ¶

### affine.apply (mlir::AffineApplyOp) ¶

affine apply operation

The affine.apply operation applies an affine mapping to a list of SSA values, yielding a single SSA value. The number of dimension and symbol arguments to affine.apply must be equal to the respective number of dimensional and symbolic inputs to the affine mapping; the affine mapping has to be one-dimensional, and so the affine.apply operation always returns one value. The input operands and result must all have ‘index’ type.

Example:

#map10 = affine_map<(d0, d1) -> (d0 floordiv 8 + d1 floordiv 128)>
...
%1 = affine.apply #map10 (%s, %t)

// Inline example.
%2 = affine.apply affine_map<(i)[s0] -> (i+s0)> (%42)[%n]


Interfaces: NoSideEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

#### Attributes: ¶

AttributeMLIR TypeDescription
map::mlir::AffineMapAttrAffineMap attribute

#### Operands: ¶

OperandDescription
mapOperandsindex

#### Results: ¶

ResultDescription
«unnamed»index

### affine.delinearize_index (mlir::AffineDelinearizeIndexOp) ¶

delinearize an index

Syntax:

operation ::= affine.delinearize_index $linear_index into   ($basis ) attr-dict : type($multi_index)  The affine.delinearize_index operation takes a single index value and calculates the multi-index according to the given basis. Example: %indices:3 = affine.delinearize_index %linear_index into (%c16, %c224, %c224) : index, index, index  In the above example, %indices:3 conceptually holds the following: #map0 = affine_map<()[s0] -> (s0 floordiv 50176)> #map1 = affine_map<()[s0] -> ((s0 mod 50176) floordiv 224)> #map2 = affine_map<()[s0] -> (s0 mod 224)> %indices_0 = affine.apply #map0()[%linear_index] %indices_1 = affine.apply #map1()[%linear_index] %indices_2 = affine.apply #map2()[%linear_index]  Interfaces: NoSideEffect (MemoryEffectOpInterface) Effects: MemoryEffects::Effect{} #### Operands: ¶ OperandDescription linear_indexindex basisindex #### Results: ¶ ResultDescription multi_indexindex ### affine.for (mlir::AffineForOp) ¶ for operation Syntax: operation ::= affine.for ssa-id = lower-bound to upper-bound (step integer-literal)? { op* } lower-bound ::= max? affine-map-attribute dim-and-symbol-use-list | shorthand-bound upper-bound ::= min? affine-map-attribute dim-and-symbol-use-list | shorthand-bound shorthand-bound ::= ssa-id | -? integer-literal  The affine.for operation represents an affine loop nest. It has one region containing its body. This region must contain one block that terminates with affine.yield. Note: when affine.for is printed in custom format, the terminator is omitted. The block has one argument of index type that represents the induction variable of the loop. The affine.for operation executes its body a number of times iterating from a lower bound to an upper bound by a stride. The stride, represented by step, is a positive constant integer which defaults to “1” if not present. The lower and upper bounds specify a half-open range: the range includes the lower bound but does not include the upper bound. The lower and upper bounds of a affine.for operation are represented as an application of an affine mapping to a list of SSA values passed to the map. The same restrictions hold for these SSA values as for all bindings of SSA values to dimensions and symbols. The affine mappings for the bounds may return multiple results, in which case the max/min keywords are required (for the lower/upper bound respectively), and the bound is the maximum/minimum of the returned values. There is no semantic ambiguity, but MLIR syntax requires the use of these keywords to make things more obvious to human readers. Many upper and lower bounds are simple, so MLIR accepts two custom form syntaxes: the form that accepts a single ‘ssa-id’ (e.g. %N) is shorthand for applying that SSA value to a function that maps a single symbol to itself, e.g., ()[s]->(s)()[%N]. The integer literal form (e.g. -42) is shorthand for a nullary mapping function that returns the constant value (e.g. ()->(-42)()). Example showing reverse iteration of the inner loop: #map57 = affine_map<(d0)[s0] -> (s0 - d0 - 1)> func.func @simple_example(%A: memref<?x?xf32>, %B: memref<?x?xf32>) { %N = dim %A, 0 : memref<?x?xf32> affine.for %i = 0 to %N step 1 { affine.for %j = 0 to %N { // implicitly steps by 1 %0 = affine.apply #map57(%j)[%N] %tmp = call @F1(%A, %i, %0) : (memref<?x?xf32>, index, index)->(f32) call @F2(%tmp, %B, %i, %0) : (f32, memref<?x?xf32>, index, index)->() } } return }  affine.for can also operate on loop-carried variables (iter_args) and return the final values after loop termination. The initial values of the variables are passed as additional SSA operands to the affine.for following the operands for the loop’s lower and upper bounds. The operation’s region has equivalent arguments for each variable representing the value of the variable at the current iteration. The region must terminate with an affine.yield that passes all the current iteration variables to the next iteration, or to the affine.for’s results if at the last iteration. For affine.for’s that execute zero iterations, the initial values of the loop-carried variables (corresponding to the SSA operands) will be the op’s results. For example, to sum-reduce a memref: func.func @reduce(%buffer: memref<1024xf32>) -> (f32) { // Initial sum set to 0. %sum_0 = arith.constant 0.0 : f32 // iter_args binds initial values to the loop's region arguments. %sum = affine.for %i = 0 to 10 step 2 iter_args(%sum_iter = %sum_0) -> (f32) { %t = affine.load %buffer[%i] : memref<1024xf32> %sum_next = arith.addf %sum_iter, %t : f32 // Yield current iteration sum to next iteration %sum_iter or to %sum // if final iteration. affine.yield %sum_next : f32 } return %sum : f32 }  %res:2 = affine.for %i = 0 to 128 iter_args(%arg0 = %init0, %arg1 = %init1) -> (index, index) { %y0 = arith.addi %arg0, %c1 : index %y1 = arith.addi %arg1, %c2 : index affine.yield %y0, %y1 : index, index }  If the affine.for defines any values, a yield terminator must be explicitly present. The number and types of the “affine.for” results must match the initial values in the iter_args binding and the yield operands. Traits: AutomaticAllocationScope, ImplicitAffineTerminator, RecursiveSideEffects Interfaces: LoopLikeOpInterface, RegionBranchOpInterface #### Operands: ¶ OperandDescription «unnamed»any type #### Results: ¶ ResultDescription resultsany type ### affine.if (mlir::AffineIfOp) ¶ if-then-else operation Syntax: operation ::= affine.if if-op-cond { op* } (else { op* })? if-op-cond ::= integer-set-attr dim-and-symbol-use-list  The affine.if operation restricts execution to a subset of the loop iteration space defined by an integer set (a conjunction of affine constraints). A single affine.if may end with an optional else clause. The condition of the affine.if is represented by an integer set (a conjunction of affine constraints), and the SSA values bound to the dimensions and symbols in the integer set. The same restrictions hold for these SSA values as for all bindings of SSA values to dimensions and symbols. The affine.if operation contains two regions for the “then” and “else” clauses. affine.if may return results that are defined in its regions. The values defined are determined by which execution path is taken. Each region of the affine.if must contain a single block with no arguments, and be terminated by affine.yield. If affine.if defines no values, the affine.yield can be left out, and will be inserted implicitly. Otherwise, it must be explicit. If no values are defined, the else block may be empty (i.e. contain no blocks). Example: #set = affine_set<(d0, d1)[s0]: (d0 - 10 >= 0, s0 - d0 - 9 >= 0, d1 - 10 >= 0, s0 - d1 - 9 >= 0)> func.func @reduced_domain_example(%A, %X, %N) : (memref<10xi32>, i32, i32) { affine.for %i = 0 to %N { affine.for %j = 0 to %N { %0 = affine.apply #map42(%j) %tmp = call @S1(%X, %i, %0) affine.if #set(%i, %j)[%N] { %1 = affine.apply #map43(%i, %j) call @S2(%tmp, %A, %i, %1) } } } return }  Example with an explicit yield (initialization with edge padding): #interior = affine_set<(i, j) : (i - 1 >= 0, j - 1 >= 0, 10 - i >= 0, 10 - j >= 0)> (%i, %j) func.func @pad_edges(%I : memref<10x10xf32>) -> (memref<12x12xf32) { %O = alloc memref<12x12xf32> affine.parallel (%i, %j) = (0, 0) to (12, 12) { %1 = affine.if #interior (%i, %j) { %2 = load %I[%i - 1, %j - 1] : memref<10x10xf32> affine.yield %2 } else { %2 = arith.constant 0.0 : f32 affine.yield %2 : f32 } affine.store %1, %O[%i, %j] : memref<12x12xf32> } return %O }  Traits: ImplicitAffineTerminator, NoRegionArguments, RecursiveSideEffects #### Operands: ¶ OperandDescription «unnamed»any type #### Results: ¶ ResultDescription resultsany type ### affine.load (mlir::AffineLoadOp) ¶ affine load operation The “affine.load” op reads an element from a memref, where the index for each memref dimension is an affine expression of loop induction variables and symbols. The output of ‘affine.load’ is a new value with the same type as the elements of the memref. An affine expression of loop IVs and symbols must be specified for each dimension of the memref. The keyword ‘symbol’ can be used to indicate SSA identifiers which are symbolic. Example 1: %1 = affine.load %0[%i0 + 3, %i1 + 7] : memref<100x100xf32>  Example 2: Uses ‘symbol’ keyword for symbols ‘%n’ and ‘%m’. %1 = affine.load %0[%i0 + symbol(%n), %i1 + symbol(%m)] : memref<100x100xf32>  Traits: MemRefsNormalizable Interfaces: AffineMapAccessInterface, AffineReadOpInterface #### Operands: ¶ OperandDescription memrefmemref of any type values indicesindex #### Results: ¶ ResultDescription resultany type ### affine.max (mlir::AffineMaxOp) ¶ max operation The “max” operation computes the maximum value result from a multi-result affine map. Example: %0 = affine.max (d0) -> (1000, d0 + 512) (%i0) : index  Interfaces: NoSideEffect (MemoryEffectOpInterface) Effects: MemoryEffects::Effect{} #### Attributes: ¶ AttributeMLIR TypeDescription map::mlir::AffineMapAttrAffineMap attribute #### Operands: ¶ OperandDescription operandsindex #### Results: ¶ ResultDescription «unnamed»index ### affine.min (mlir::AffineMinOp) ¶ min operation Syntax: operation ::= ssa-id = affine.min affine-map-attribute dim-and-symbol-use-list  The affine.min operation applies an affine mapping to a list of SSA values, and returns the minimum value of all result expressions. The number of dimension and symbol arguments to affine.min must be equal to the respective number of dimensional and symbolic inputs to the affine mapping; the affine.min operation always returns one value. The input operands and result must all have ‘index’ type. Example: %0 = affine.min affine_map<(d0)[s0] -> (1000, d0 + 512, s0)> (%arg0)[%arg1]  Interfaces: NoSideEffect (MemoryEffectOpInterface) Effects: MemoryEffects::Effect{} #### Attributes: ¶ AttributeMLIR TypeDescription map::mlir::AffineMapAttrAffineMap attribute #### Operands: ¶ OperandDescription operandsindex #### Results: ¶ ResultDescription «unnamed»index ### affine.parallel (mlir::AffineParallelOp) ¶ multi-index parallel band operation The “affine.parallel” operation represents a hyper-rectangular affine parallel band, defining zero or more SSA values for its induction variables. It has one region capturing the parallel band body. The induction variables are represented as arguments of this region. These SSA values always have type index, which is the size of the machine word. The strides, represented by steps, are positive constant integers which defaults to “1” if not present. The lower and upper bounds specify a half-open range: the range includes the lower bound but does not include the upper bound. The body region must contain exactly one block that terminates with “affine.yield”. The lower and upper bounds of a parallel operation are represented as an application of an affine mapping to a list of SSA values passed to the map. The same restrictions hold for these SSA values as for all bindings of SSA values to dimensions and symbols. The list of expressions in each map is interpreted according to the respective bounds group attribute. If a single expression belongs to the group, then the result of this expression is taken as a lower(upper) bound of the corresponding loop induction variable. If multiple expressions belong to the group, then the lower(upper) bound is the max(min) of these values obtained from these expressions. The loop band has as many loops as elements in the group bounds attributes. Each value yielded by affine.yield will be accumulated/reduced via one of the reduction methods defined in the AtomicRMWKind enum. The order of reduction is unspecified, and lowering may produce any valid ordering. Loops with a 0 trip count will produce as a result the identity value associated with each reduction (i.e. 0.0 for addf, 1.0 for mulf). Assign reductions for loops with a trip count != 1 produces undefined results. Note: Calling AffineParallelOp::build will create the required region and block, and insert the required terminator if it is trivial (i.e. no values are yielded). Parsing will also create the required region, block, and terminator, even when they are missing from the textual representation. Example (3x3 valid convolution): func.func @conv_2d(%D : memref<100x100xf32>, %K : memref<3x3xf32>) -> (memref<98x98xf32>) { %O = alloc memref<98x98xf32> affine.parallel (%x, %y) = (0, 0) to (98, 98) { %0 = affine.parallel (%kx, %ky) = (0, 0) to (2, 2) reduce ("addf") { %1 = affine.load %D[%x + %kx, %y + %ky] : memref<100x100xf32> %2 = affine.load %K[%kx, %ky] : memref<3x3xf32> %3 = arith.mulf %1, %2 : f32 affine.yield %3 : f32 } affine.store %0, O[%x, %y] : memref<98x98xf32> } return %O }  Example (tiling by potentially imperfectly dividing sizes): affine.parallel (%ii, %jj) = (0, 0) to (%N, %M) step (32, 32) { affine.parallel (%i, %j) = (%ii, %jj) to (min(%ii + 32, %N), min(%jj + 32, %M)) { call @f(%i, %j) : (index, index) -> () } }  Traits: AutomaticAllocationScope, ImplicitAffineTerminator, MemRefsNormalizable, RecursiveSideEffects Interfaces: LoopLikeOpInterface #### Attributes: ¶ AttributeMLIR TypeDescription reductions::mlir::ArrayAttrReduction ops lowerBoundsMap::mlir::AffineMapAttrAffineMap attribute lowerBoundsGroups::mlir::DenseIntElementsAttr32-bit signless integer elements attribute upperBoundsMap::mlir::AffineMapAttrAffineMap attribute upperBoundsGroups::mlir::DenseIntElementsAttr32-bit signless integer elements attribute steps::mlir::ArrayAttr64-bit integer array attribute #### Operands: ¶ OperandDescription mapOperandsindex #### Results: ¶ ResultDescription resultsany type ### affine.prefetch (mlir::AffinePrefetchOp) ¶ affine prefetch operation The “affine.prefetch” op prefetches data from a memref location described with an affine subscript similar to affine.load, and has three attributes: a read/write specifier, a locality hint, and a cache type specifier as shown below: affine.prefetch %0[%i, %j + 5], read, locality<3>, data : memref<400x400xi32>  The read/write specifier is either ‘read’ or ‘write’, the locality hint specifier ranges from locality<0> (no locality) to locality<3> (extremely local keep in cache). The cache type specifier is either ‘data’ or ‘instr’ and specifies whether the prefetch is performed on data cache or on instruction cache. Interfaces: AffineMapAccessInterface #### Attributes: ¶ AttributeMLIR TypeDescription isWrite::mlir::BoolAttrbool attribute localityHint::mlir::IntegerAttr32-bit signless integer attribute whose minimum value is 0 whose maximum value is 3 isDataCache::mlir::BoolAttrbool attribute #### Operands: ¶ OperandDescription memrefmemref of any type values indicesindex ### affine.store (mlir::AffineStoreOp) ¶ affine store operation The “affine.store” op writes an element to a memref, where the index for each memref dimension is an affine expression of loop induction variables and symbols. The ‘affine.store’ op stores a new value which is the same type as the elements of the memref. An affine expression of loop IVs and symbols must be specified for each dimension of the memref. The keyword ‘symbol’ can be used to indicate SSA identifiers which are symbolic. Example 1: affine.store %v0, %0[%i0 + 3, %i1 + 7] : memref<100x100xf32>  Example 2: Uses ‘symbol’ keyword for symbols ‘%n’ and ‘%m’. affine.store %v0, %0[%i0 + symbol(%n), %i1 + symbol(%m)] : memref<100x100xf32>  Traits: MemRefsNormalizable Interfaces: AffineMapAccessInterface, AffineWriteOpInterface #### Operands: ¶ OperandDescription valueany type memrefmemref of any type values indicesindex ### affine.vector_load (mlir::AffineVectorLoadOp) ¶ affine vector load operation The “affine.vector_load” is the vector counterpart of affine.load. It reads a slice from a MemRef, supplied as its first operand, into a vector of the same base elemental type. The index for each memref dimension is an affine expression of loop induction variables and symbols. These indices determine the start position of the read within the memref. The shape of the return vector type determines the shape of the slice read from the memref. This slice is contiguous along the respective dimensions of the shape. Strided vector loads will be supported in the future. An affine expression of loop IVs and symbols must be specified for each dimension of the memref. The keyword ‘symbol’ can be used to indicate SSA identifiers which are symbolic. Example 1: 8-wide f32 vector load. %1 = affine.vector_load %0[%i0 + 3, %i1 + 7] : memref<100x100xf32>, vector<8xf32>  Example 2: 4-wide f32 vector load. Uses ‘symbol’ keyword for symbols ‘%n’ and ‘%m’. %1 = affine.vector_load %0[%i0 + symbol(%n), %i1 + symbol(%m)] : memref<100x100xf32>, vector<4xf32>  Example 3: 2-dim f32 vector load. %1 = affine.vector_load %0[%i0, %i1] : memref<100x100xf32>, vector<2x8xf32>  TODOs: • Add support for strided vector loads. • Consider adding a permutation map to permute the slice that is read from memory (see vector.transfer_read). Traits: MemRefsNormalizable Interfaces: AffineMapAccessInterface, AffineReadOpInterface #### Operands: ¶ OperandDescription memrefmemref of any type values indicesindex #### Results: ¶ ResultDescription resultvector of any type values ### affine.vector_store (mlir::AffineVectorStoreOp) ¶ affine vector store operation The “affine.vector_store” is the vector counterpart of affine.store. It writes a vector, supplied as its first operand, into a slice within a MemRef of the same base elemental type, supplied as its second operand. The index for each memref dimension is an affine expression of loop induction variables and symbols. These indices determine the start position of the write within the memref. The shape of th input vector determines the shape of the slice written to the memref. This slice is contiguous along the respective dimensions of the shape. Strided vector stores will be supported in the future. An affine expression of loop IVs and symbols must be specified for each dimension of the memref. The keyword ‘symbol’ can be used to indicate SSA identifiers which are symbolic. Example 1: 8-wide f32 vector store. affine.vector_store %v0, %0[%i0 + 3, %i1 + 7] : memref<100x100xf32>, vector<8xf32>  Example 2: 4-wide f32 vector store. Uses ‘symbol’ keyword for symbols ‘%n’ and ‘%m’. affine.vector_store %v0, %0[%i0 + symbol(%n), %i1 + symbol(%m)] : memref<100x100xf32>, vector<4xf32>  Example 3: 2-dim f32 vector store. affine.vector_store %v0, %0[%i0, %i1] : memref<100x100xf32>, vector<2x8xf32>  TODOs: • Add support for strided vector stores. • Consider adding a permutation map to permute the slice that is written to memory (see vector.transfer_write). Traits: MemRefsNormalizable Interfaces: AffineMapAccessInterface, AffineWriteOpInterface #### Operands: ¶ OperandDescription valuevector of any type values memrefmemref of any type values indicesindex ### affine.yield (mlir::AffineYieldOp) ¶ Yield values to parent operation Syntax: operation ::= affine.yield attr-dict ($operands^ : type(\$operands))?


“affine.yield” yields zero or more SSA values from an affine op region and terminates the region. The semantics of how the values yielded are used is defined by the parent operation. If “affine.yield” has any operands, the operands must match the parent operation’s results. If the parent operation defines no values, then the “affine.yield” may be left out in the custom syntax and the builders will insert one implicitly. Otherwise, it has to be present in the syntax to indicate which values are yielded.


Traits: MemRefsNormalizable, ReturnLike, Terminator

Interfaces: NoSideEffect (MemoryEffectOpInterface)

Effects: MemoryEffects::Effect{}

#### Operands:

| Operand | Description |
| :-----: | ----------- |
| operands | any type

Syntax:



operation ::= ssa-id = affine.load ssa-use [ multi-dim-affine-map-of-ssa-ids ] : memref-type


The affine.load op reads an element from a memref, where the index for each
memref dimension is an affine expression of loop induction variables and
symbols. The output of 'affine.load' is a new value with the same type as the
elements of the memref. An affine expression of loop IVs and symbols must be
specified for each dimension of the memref. The keyword 'symbol' can be used to
indicate SSA identifiers which are symbolic.

Example:

mlir

Example 1:

%1 = affine.load %0[%i0 + 3, %i1 + 7] : memref<100x100xf32>

Example 2: Uses 'symbol' keyword for symbols '%n' and '%m'.

%1 = affine.load %0[%i0 + symbol(%n), %i1 + symbol(%m)]
: memref<100x100xf32>



### ‘affine.store’ operation ¶

Syntax:

operation ::= ssa-id = affine.store ssa-use, ssa-use [ multi-dim-affine-map-of-ssa-ids ] : memref-type


The affine.store op writes an element to a memref, where the index for each memref dimension is an affine expression of loop induction variables and symbols. The ‘affine.store’ op stores a new value which is the same type as the elements of the memref. An affine expression of loop IVs and symbols must be specified for each dimension of the memref. The keyword ‘symbol’ can be used to indicate SSA identifiers which are symbolic.

Example:


Example 1:

affine.store %v0, %0[%i0 + 3, %i1 + 7] : memref<100x100xf32>

Example 2: Uses 'symbol' keyword for symbols '%n' and '%m'.

affine.store %v0, %0[%i0 + symbol(%n), %i1 + symbol(%m)]
: memref<100x100xf32>



### ‘affine.dma_start’ operation ¶

Syntax:

operation ::= affine.dma_Start ssa-use [ multi-dim-affine-map-of-ssa-ids ], [ multi-dim-affine-map-of-ssa-ids ], [ multi-dim-affine-map-of-ssa-ids ], ssa-use : memref-type


The affine.dma_start op starts a non-blocking DMA operation that transfers data from a source memref to a destination memref. The source and destination memref need not be of the same dimensionality, but need to have the same elemental type. The operands include the source and destination memref’s each followed by its indices, size of the data transfer in terms of the number of elements (of the elemental type of the memref), a tag memref with its indices, and optionally at the end, a stride and a number_of_elements_per_stride arguments. The tag location is used by an AffineDmaWaitOp to check for completion. The indices of the source memref, destination memref, and the tag memref have the same restrictions as any affine.load/store. In particular, index for each memref dimension must be an affine expression of loop induction variables and symbols. The optional stride arguments should be of ‘index’ type, and specify a stride for the slower memory space (memory space with a lower memory space id), transferring chunks of number_of_elements_per_stride every stride until %num_elements are transferred. Either both or no stride arguments should be specified. The value of ‘num_elements’ must be a multiple of ‘number_of_elements_per_stride’.

Example:

For example, a DmaStartOp operation that transfers 256 elements of a memref
'%src' in memory space 0 at indices [%i + 3, %j] to memref '%dst' in memory
space 1 at indices [%k + 7, %l], would be specified as follows:

%num_elements = arith.constant 256
%idx = arith.constant 0 : index
%tag = memref.alloc() : memref<1xi32, 4>
affine.dma_start %src[%i + 3, %j], %dst[%k + 7, %l], %tag[%idx],
%num_elements :
memref<40x128xf32, 0>, memref<2x1024xf32, 1>, memref<1xi32, 2>

If %stride and %num_elt_per_stride are specified, the DMA is expected to
transfer %num_elt_per_stride elements every %stride elements apart from
memory space 0 until %num_elements are transferred.

affine.dma_start %src[%i, %j], %dst[%k, %l], %tag[%idx], %num_elements,
%stride, %num_elt_per_stride : ...


### ‘affine.dma_wait’ operation ¶

Syntax:

operation ::= affine.dma_Start ssa-use [ multi-dim-affine-map-of-ssa-ids ], [ multi-dim-affine-map-of-ssa-ids ], [ multi-dim-affine-map-of-ssa-ids ], ssa-use : memref-type


The affine.dma_start op blocks until the completion of a DMA operation associated with the tag element ‘%tag[%index]’. %tag is a memref, and %index has to be an index with the same restrictions as any load/store index. In particular, index for each memref dimension must be an affine expression of loop induction variables and symbols. %num_elements is the number of elements associated with the DMA operation. For example:

Example:

affine.dma_start %src[%i, %j], %dst[%k, %l], %tag[%index], %num_elements :
memref<2048xf32, 0>, memref<256xf32, 1>, memref<1xi32, 2>
...
...
affine.dma_wait %tag[%index], %num_elements : memref<1xi32, 2>
`